CN103353588A - Two-dimensional DOA (direction of arrival) angle estimation method based on antenna uniform planar array - Google Patents

Abstract

The invention discloses a two-dimensional DOA (direction of arrival) angle estimation method based on an antenna uniform planar array, and mainly solves problems of slow response speeds in target detection and passive location and big estimation errors which are caused by large computation amount of direction angle estimation in the prior art. The method comprises realization steps of forming a uniform planar array by using antenna receivers; calculating echo signals of all the antenna receivers; calculating noise subspaces of the echo signals of the antenna receivers; substituting a one-dimensional angle which is set to be a fixed value into an angle solving function to obtain another one-dimensional angle value, and obtaining multiple groups of values through multiple computations; generating an amplitude spectra by using the multiple groups of angle values; and obtaining two-dimensional angle values of the antenna uniform planar array by searching peak points in the amplitude spectra. According to the method, the two-dimensional DOA angle estimation is simplified into a process of one-dimensional DOA angle estimation, and thus the computation amount is substantially reduced, speeds in target detection and passive location response are improved, parameter estimation errors caused by information delay are prevented, and accordingly the method can be applied to rapid target detection and passive location.

Description

2-d direction finding angle method of estimation based on antenna uniform planar battle array

Technical field

The invention belongs to the signal processing technology field, particularly a kind of 2-d direction finding angle method of estimation based on antenna uniform planar battle array can be used for target reconnaissance and passive location.

Background technology

DOA estimation in direction of arrival angle is the signal that utilizes the signal source of a plurality of different directions of aerial signal array received that are in the space diverse location to send, use the modern signal processing method to estimate fast and accurately the direction of signal source, have significant application value in fields such as radar, sonar, radio communications.2-d direction finding is estimated the estimation of general employing face battle array or vector sensor realization two-dimensional parameter, most efficient 2-d DOA estimation algorithms belong to the direct expansion of one dimension DOA estimation algorithm, do not take full advantage of the multidimensional information of carrying in the array received signal, often exist operand excessive or have shortcomings such as angle pairing.

Traditional two dimensional angle method of estimation comprises two kinds: a kind of is to utilize the two dimension angular search to obtain simultaneously two dimension angular; Another kind is to ask for respectively wherein one dimension angle value, carries out the angle pairing again.First method need to be used two-dimensional search, its operand be linear search square doubly, so operand is huge; Second method also needs use angle pairing algorithm after finishing respectively the one dimension angle estimation, this process still needs to spend certain operand, so these two kinds of methods all have than the macrooperation amount.In the practical application, target reconnaissance and passive location all need to be carried out on the basis of angle estimation, if the angle estimation arithmetic speed will cause target reconnaissance and passive location reaction velocity slow slowly, even cause because the parameter estimating error that information delay causes is larger.

Summary of the invention

The object of the invention is to the deficiency for above-mentioned prior art, a kind of 2-d direction finding angle method of estimation based on antenna uniform planar battle array is proposed, with the operand that significantly reduces to estimate, improve target reconnaissance and passive location reaction velocity, avoid the parameter estimating error that causes because of information delay.

For achieving the above object, performing step of the present invention comprises as follows:

1) adopt aerial receiver to form the uniform planar battle array, wherein the x direction of principal axis has N aerial receiver, and the y direction of principal axis has M aerial receiver, and the aerial receiver spacing is d, N 〉=2, and M 〉=2,0＜d≤λ/2, λ is incident narrow band signal wavelength;

2) with I incoherent narrow band signal s _i(t) with 2-d direction finding angle (α _i, β _i) incide on the antenna uniform planar battle array, wherein, i=1,2 ..., I, 1≤I＜NM, α _iRepresent the incident direction of i narrow band signal to be asked and the angle of x axle, β _iRepresent the incident direction of i narrow band signal to be asked and the angle of y axle, and α _i∈ (0 °, 180 °], β _i∈ (0 °, 180 °];

3) the echoed signal Y (t) of all aerial receivers on the calculating antenna uniform planar battle array;

$Y\left(t\right)=\underset{i=1}{\overset{I}{\mathrm{\Σ}}}\underset{m=0}{\overset{M-1}{\mathrm{\Σ}}}\underset{n=0}{\overset{N-1}{\mathrm{\Σ}}}[a_n\left({\mathrm{\α}}_i\right)\⊗a_m\left({\mathrm{\β}}_i\right)]\·s_i\left(t\right)+N\left(t\right)$

Wherein, N (t) is the noise signal vector, a _n(α _i) and a _m(β _i) represent respectively the two dimension angular α of the narrow band signal of i incident _iAnd β _iCorresponding direction vector, the expansion form is expressed as:

a _n(α _i)=(1,exp(j2πd·cosα _i/λ),...,exp[j2πd·(N-1)·cosα _i/λ]) ^T

a _m(β _i)=(1,exp(j2πd·cosβ _i/λ),...,exp[j2πd·(M-1)·cosβ _i/λ]) ^T

4) the noise subspace U of calculating aerial receiver echoed signal Y (t) _n

5) structure angle solved function minV (α _i, β _i), V (α wherein _i, β _i) be:

$V({\mathrm{\α}}_i,{\mathrm{\β}}_i)=a_m^H\left({\mathrm{\β}}_i\right)G\left({\mathrm{\α}}_i\right)a_m\left({\mathrm{\β}}_i\right)$

Wherein, $G\left({\mathrm{\α}}_i\right)=[a_n\left({\mathrm{\α}}_i\right)\⊗I_M{]}^H{U}_n{U}_n^H[a_n\left({\mathrm{\α}}_i\right)\⊗I_M]$ Be intermediate variable;

6) establish α _iFor (0 °, 180 °] an interior fixed value of scope, according to angle solved function minV (α _i, β _i), obtain as follows β _iValue:

6a) definition intermediate variable b _i=exp (j2 π dcos β _i/ λ), and with its substitution formula V (α _i, β _i) in, obtain formula V (α _i, b _i), to b _iDifferentiate

Obtain 2M-2 root;

6b) exist

2M-2 root in seek amplitude near 1 root as b _iValue, again with this b _iThe following formula of substitution calculates corresponding β _iValue:

${\mathrm{\β}}_i=\arccos \left(\frac{\mathrm{\λ}}{2\mathrm{\πd}}\arg \left(b_i\right)\right);$

7) α _iGet (0 °, 180 °] other interior fixed value of scope, repeated execution of steps 6), obtain corresponding β _iValue;

Many groups α that 8) will obtain _iAnd β _iSubstitution function 1/V (α _i, β _i) obtain corresponding a plurality of V values, in the plane, be origin with (0,0), with many groups of (α _i, V) being x, the y coordinate is drawn the range value point, and each point is linked to each other, and obtains the amplitude spectrogram;

9) seek front I larger spectrum peak of amplitude according to order from high to low from the amplitude spectrogram, the x coordinate that the peak point at these spectrum peaks is corresponding is as the α that tries to achieve _iValue is used these α _iCorresponding β _iAs the β that tries to achieve _iValue is finished based on the 2-d direction finding angle of antenna uniform planar battle array and is estimated.

The present invention is owing to become one-dimensional wave to reach the orientation angle estimation procedure two dimensional angle estimation procedure abbreviation, only need the one dimension angle searching can obtain simultaneously two dimensional angle, two dimension angular search or angle pairing process have been avoided, reduce computational complexity, improved arithmetic speed.

Experimental result shows that the operand of Two-dimensional direction of arrival angle angle of the present invention only is Ο { LM ²N ²+ M ³N ³+ n[(M ²N+M ²) (MN-I)+MN+M+M ²], and the operand of traditional 2D-MUSIC method Two-dimensional direction of arrival angle angle is Ο { LM ²N ²+ M ³N ³+ n ²[MN (MN-I)] }, α wherein _iWith β _iSearch point be n, n 〉=1, because x direction of principal axis receiver quantity N, y direction of principal axis receiver quantity M, narrow band signal quantity I and fast umber of beats L all are much smaller than n, as seen the arithmetic speed of the inventive method is far above traditional 2D-MUSIC method, can to target reconnaissance and passive location improves reaction velocity and the parameter estimation accuracy plays a driving role.

Description of drawings

Fig. 1 is realization flow figure of the present invention;

Fig. 2 is the operand comparison diagram of the present invention and existing 2D-MUSIC algorithm;

Fig. 3 is the α angle estimation root-mean-square error comparison diagram of the present invention and existing 2D-MUSIC algorithm;

Fig. 4 is the β angle estimation root-mean-square error comparison diagram of the present invention and existing 2D-MUSIC algorithm.

Embodiment

With reference to Fig. 1, two dimensional angle of the present invention estimates that implementation step is as follows:

Step 1: utilize aerial receiver to form the uniform planar battle array.

Place 1 aerial receiver at the x direction of principal axis every spacing d, place altogether N, be referred to as 1 row aerial receiver; Place 1 row aerial receiver at the y direction of principal axis every spacing d, it is capable to place altogether M, and forming the total number of aerial receiver is the antenna uniform planar battle array of NM, N 〉=2 wherein, and M 〉=2,0＜d≤λ/2, λ is incident narrow band signal wavelength;

Step 2: narrow band signal is incided on the antenna uniform planar battle array.

If the narrow band signal that incides on the antenna uniform planar battle array is I, and uncorrelated between the signal, signal form s _i(t) expression;

Described narrow band signal satisfies following condition:

B·ΔT _max<<1，

Wherein B represents signal bandwidth, Δ T _MaxThe expression signal arrives the maximal value of the delay inequality of any two aerial receivers;

Described narrow band signal is from space any direction directive antenna uniform planar battle array, and this incident direction can be regarded as a ray, and the angle that this ray and plane, antenna uniform planar battle array place form is called the 2-d direction finding angle, with (α _i, β _i) expression, wherein, i=1,2 ..., I, 1≤I＜NM, α _iRepresent the incident direction of i incident narrow band signal and the angle of x axle, β _iRepresent the incident direction of i incident narrow band signal and the angle of y axle, and α _i∈ (0 °, 180 °], β _i∈ (0 °, 180 °].Requiring narrow band signal number I among the present invention is known value, α _iAnd β _iIt is value to be estimated.

Step 3: the echoed signal Y (t) that calculates all aerial receivers on the antenna uniform planar battle array.

3a) calculate the individual signals s that each aerial receiver receives on the antenna uniform planar battle array _i(t) with corresponding direction vector

Product y _{N, m, i}(t):

$y_{n,m,i}\left(t\right)=[a_n\left({\mathrm{\&alpha;}}_i\right)\&CircleTimes;a_m\left({\mathrm{\&beta;}}_i\right)]\&CenterDot;s_i\left(t\right),$

A wherein _n(α _i) and a _m(β _i) represent respectively the two dimension angular α of the narrow band signal of i incident _iAnd β _iCorresponding direction vector, its expansion form is expressed as:

a _n(α _i)=(1,exp(j2πd·cosα _i/λ),...,exp[j2πd·(N-1)·cosα _i/λ]) ^T

a _m(β _i)=(1,exp(j2πd·cosβ _i/λ),...,exp[j2πd·(M-1)·cosβ _i/λ]) ^T

Wherein,

Be the Kronecker multiplication of matrix, T is matrix transpose;

The signal of a plurality of signals that 3b) all receivers on the antenna uniform planar battle array received and direction vector product y _{N, m, i}(t) addition generates total echoed signal Y ' (t):

$Y^{\&prime;}\left(t\right)=\underset{i=1}{\overset{I}{\mathrm{\&Sigma;}}}\underset{m=0}{\overset{M-1}{\mathrm{\&Sigma;}}}\underset{n=0}{\overset{N-1}{\mathrm{\&Sigma;}}}[a_n\left({\mathrm{\&alpha;}}_i\right)\&CircleTimes;a_m\left({\mathrm{\&beta;}}_i\right)]\&CenterDot;s_i\left(t\right)$

3c) consider the impact of noise factor, final echoed signal Y (t) be expressed as:

$Y\left(t\right)=\underset{i=1}{\overset{I}{\mathrm{\&Sigma;}}}\underset{m=0}{\overset{M-1}{\mathrm{\&Sigma;}}}\underset{n=0}{\overset{N-1}{\mathrm{\&Sigma;}}}[a_n\left({\mathrm{\&alpha;}}_i\right)\&CircleTimes;a_m\left({\mathrm{\&beta;}}_i\right)]\&CenterDot;s_i\left(t\right)+N\left(t\right)$

Wherein, N (t) is the noise signal vector, and signal to noise ratio (S/N ratio) is less, and is larger to the evaluated error of direction of arrival angle.

Step 4: the noise subspace U that calculates aerial receiver echoed signal Y (t) _n

4a) covariance matrix R=E[Y (t) Y (t) of calculating aerial receiver signal ^H], E[wherein] to ask mathematical expectation, H be the Matrix Conjugate transposition in expression;

4b) covariance matrix R is carried out feature decomposition, that is:

$R=U_s{\mathrm{\&Lambda;}}_s{U}_s^H+U_n{\mathrm{\&Lambda;}}_n{U}_n^H,$

Wherein, Λ _sBe I the eigenvalue matrix that large eigenwert forms of covariance matrix R, Λ _nBe the eigenvalue matrix that covariance matrix R (NM-I) individual little eigenwert forms, U _sFor I the large corresponding feature matrix of eigenwert, be defined as signal subspace, U _nFor the corresponding feature matrix of (NM-I) individual little eigenwert, be defined as noise subspace.

Step 5: structure angle solved function minV (α _i, β _i).

5a) defined function V (α _i, β _i) be:

$V({\mathrm{\&alpha;}}_i,{\mathrm{\&beta;}}_i)={[a_n\left({\mathrm{\&alpha;}}_i\right)\&CircleTimes;a_m\left({\mathrm{\&beta;}}_i\right)]}^H{U}_n{U}_n^H[a_n\left({\mathrm{\&alpha;}}_i\right)\&CircleTimes;a_m\left({\mathrm{\&beta;}}_i\right)];$

5b) with above-mentioned steps 5a) in equation be deformed into:

$V({\mathrm{\&alpha;}}_i,{\mathrm{\&beta;}}_i)={a_m^H\left({\mathrm{\&beta;}}_i\right)[a_n\left({\mathrm{\&alpha;}}_i\right)\&CircleTimes;I_m]}^H{U}_n{U}_n^H[a_n\left({\mathrm{\&alpha;}}_i\right)\&CircleTimes;I_m]a_m\left({\mathrm{\&beta;}}_i\right);$

5c) make intermediate variable $G\left({\mathrm{\&alpha;}}_i\right)=[a_n\left({\mathrm{\&alpha;}}_i\right)\&CircleTimes;I_M{]}^H{U}_n{U}_n^H[a_n\left({\mathrm{\&alpha;}}_i\right)\&CircleTimes;I_M],$ With above-mentioned steps 5b) in equation be reduced to:

$V({\mathrm{\&alpha;}}_i,{\mathrm{\&beta;}}_i)=a_m^H\left({\mathrm{\&beta;}}_i\right)G\left({\mathrm{\&alpha;}}_i\right)a_m\left({\mathrm{\&beta;}}_i\right);$

5d) according to above-mentioned steps 5c) in equation V (α _i, β _i), structure angle solved function minV (α _i, β _i),

Wherein, the function minimal value is asked in min () expression.

Step 6: establish α _iFor (0 °, 180 °] an interior fixed value of scope, according to angle solved function minV (α _i, β _i) find the solution β _iValue.

6a) definition intermediate variable b _i=exp (j2 π dcos β _i/ λ), and with its substitution formula V (α _i, β _i) in, with wherein all formula exp (j2 π dcos β _i/ λ) use b _iSubstitute, obtain formula V (α _i, b _i), to b _iDifferentiate

Obtain 2M-2 root, concrete steps are:

6a1) with formula V (α _i, b _i) expand into:

Wherein, g ₁₁, g ₁₂... g _MMBe intermediate variable G (α _i) each element in the matrix;

6a2) according to formula V (α _i, b _i) expansion, with formula V (α _i, b _i) to b _iDifferentiate

Expand into:

$\frac{\&PartialD;}{\&PartialD;b_i}V(a_i,b_i)=(M-1)g_{1M}{b}_i^{M-2}+\&CenterDot;\&CenterDot;\&CenterDot;+(g_{12}+g_{23}+\&CenterDot;\&CenterDot;\&CenterDot;g_{(M-1)M})+0+$

$(-1)(g_{21}+g_{32}+\&CenterDot;\&CenterDot;\&CenterDot;g_{M(M-1)})b_i^{-2}+\&CenterDot;\&CenterDot;\&CenterDot;+(-M+1)g_{M1}{b}_i^{-M}=0$

Because α _iBe fixed value, so G (α _i) each element in the matrix is fixed value, and a unknown number b is only arranged in the aforesaid equation _i

6a3) above-mentioned steps 6a2) equation is 2M-2 time, therefore will obtain 2M-2 root;

6b) exist

2M-2 root in, not every all is b _iSolution, only having amplitude is that 1 root is only required b _iValue, in fact because the impact of the factor such as noise, seek amplitude near 1 root as b _iValue is again with this b _iThe following formula of substitution calculates corresponding β _iValue:

${\mathrm{\&beta;}}_i=\arccos \left(\frac{\mathrm{\&lambda;}}{2\mathrm{\&pi;d}}\arg \left(b_i\right)\right);$

Wherein, plural phase place is got in arg () expression.

Step 7: establish α _iGet (0 °, 180 °] other interior fixed value of scope, repeated execution of steps 6), obtain corresponding β _iValue.

α _iIn span, according to from small to large order, carry out value with the fixed angle interval; The value interval can be set according to the angle estimation precision that expectation reaches, and the value interval is less, and the angle estimation precision is higher.

Step 8: according to the many groups α that obtains _iAnd β _iDrafting amplitude spectrogram.

Many group α obtained above _iAnd β _iIn, only have the angle of satisfying solved function minV (α _i, β _i) I group angle value be only required two dimensional angle value, ask minV (α _i, β _i) be equivalent to ask function maximum value max[1/V (α _i, β _i)], draw the amplitude spectrogram according to this function, concrete steps are:

Many groups α that 8a) will obtain _iAnd β _iSubstitution function 1/V (α _i, β _i) the corresponding a plurality of V values of acquisition;

In the plane, be origin with (0,0) 8b), with many groups of (α _i, V) being x, the y coordinate is drawn the range value point;

8c) each range value point is linked to each other, obtain the amplitude spectrogram.

Step 9: finish 2-d direction finding angle α _iAnd β _iEstimation.

Seek front I larger spectrum peak of amplitude according to order from high to low from the amplitude spectrogram, this example is got I=3; The x coordinate that the peak point at these spectrum peaks is corresponding is as the α that tries to achieve _iValue is used these α _iCorresponding β _iAs the β that tries to achieve _iValue is finished based on the 2-d direction finding angle of antenna uniform planar battle array and is estimated.

Effect of the present invention can illustrate by following emulation:

1. simulated conditions and method:

Adopt aerial receiver to form the uniform planar battle array, wherein the x direction of principal axis has 8 aerial receivers, and the y direction of principal axis has 8 aerial receivers, and aerial receiver spacing d equals λ/2.There are three narrow band signals to incide the uniform planar battle array, wherein the value of the angle β of the angle α of narrow band signal incident direction and x axle and narrow band signal incident direction and y axle is respectively (60 °, 50 °), (90 °, 100 °) and (145 °, 75 °).Signal to noise ratio snr is 0dB, and fast umber of beats L equals 64, and the angle searching value is spaced apart 0.01 degree.

In order further to estimate performance of the present invention, to repeatedly independently experimental result carried out on average, and the root-mean-square error of employing two dimension angular is as evaluation index:

$\left\{\begin{array}{c}{\mathrm{RMSE}}_{\mathrm{\&alpha;}}=\frac{1}{I}\underset{i=1}{\overset{I}{\mathrm{\&Sigma;}}}\sqrt{\frac{1}{\mathrm{Num}}\underset{\mathrm{num}=1}{\overset{\mathrm{Num}}{\mathrm{\&Sigma;}}}{({\widehat{\mathrm{\&alpha;}}}_i-{\mathrm{\&alpha;}}_i)}^2}\\ {\mathrm{RMSE}}_{\mathrm{\&beta;}}=\frac{1}{I}\underset{i=1}{\overset{I}{\mathrm{\&Sigma;}}}\sqrt{\frac{1}{\mathrm{Num}}\underset{\mathrm{num}}{\overset{\mathrm{Num}}{\mathrm{\&Sigma;}}}}{({\widehat{\mathrm{\&beta;}}}_i-{\mathrm{\&beta;}}_i)}^2\end{array}\right.$

RMSE wherein _αAnd RMSE _βThe estimation root-mean-square error that represents respectively α and β, Num is experiment number, α _iBe the actual value of i angle,

The estimated value that represents i angle.This emulation adopts respectively the present invention and existing 2D-MUSIC algorithm to carry out.

2. emulation content and result

Emulation 1 utilizes the present invention and existing 2D-MUSIC algorithm to carry out respectively two dimensional angle and estimates, and the statistical calculation amount, and its result as shown in Figure 2.Horizontal ordinate represents the angle searching number of times among Fig. 2, and ordinate represents operand.

As can be seen from Figure 2, the present invention compares with existing 2D-MUSIC algorithm, decrease the operand of angle estimation, and along with the increase of angle searching number of times, it is larger that operand reduces amplitude.

Emulation 2 utilizes the present invention and existing 2D-MUSIC algorithm to carry out respectively independently two dimensional angle estimating experiment 100 times, calculates respectively the root-mean-square error of α angle and the root-mean-square error of β angle, and its result as shown in Figure 3 and Figure 4.Wherein Fig. 3 is for calculating the root-mean-square error of α angle, and Fig. 4 is for calculating the root-mean-square error of β angle; Horizontal ordinate represents signal to noise ratio (S/N ratio) among Fig. 3 and Fig. 4, and ordinate represents root-mean-square error, and the signal to noise ratio (S/N ratio) variation range is-2dB～8dB.

Can find out that from Fig. 3 and Fig. 4 the present invention is substantially suitable with existing 2D-MUSIC algorithm angle estimation precision.

To sum up, the present invention has significantly reduced operand when guaranteeing the angle estimation precision, guaranteed the rapid reaction of target reconnaissance and passive location, has avoided the parameter estimating error that causes because of information delay.

Claims (3)

1. 2-d direction finding angle method of estimation based on antenna uniform planar battle array may further comprise the steps:

1) adopt aerial receiver to form the uniform planar battle array, wherein the x direction of principal axis has N aerial receiver, and the y direction of principal axis has M aerial receiver, and the aerial receiver spacing is d, N 〉=2, and M 〉=2,0＜d≤λ/2, λ is incident narrow band signal wavelength;

2) with I incoherent narrow band signal s _i(t) with 2-d direction finding angle (α _i, β _i) incide on the antenna uniform planar battle array, wherein, i=1,2 ..., I, 1≤I＜NM, α _iRepresent the incident direction of i narrow band signal to be asked and the angle of x axle, β _iRepresent the incident direction of i narrow band signal to be asked and the angle of y axle, and α _i∈ (0 °, 180 °], β _i∈ (0 °, 180 °];

3) the echoed signal Y (t) of all aerial receivers on the calculating antenna uniform planar battle array;

$Y\left(t\right)=\underset{i=1}{\overset{I}{\mathrm{\&Sigma;}}}\underset{m=0}{\overset{M-1}{\mathrm{\&Sigma;}}}\underset{n=0}{\overset{N-1}{\mathrm{\&Sigma;}}}[a_n\left({\mathrm{\&alpha;}}_i\right)\&CircleTimes;a_m\left({\mathrm{\&beta;}}_i\right)]\&CenterDot;s_i\left(t\right)+N\left(t\right)$

Wherein, N (t) is the noise signal vector, a _n(α _i) and a _m(β _i) represent respectively the two dimension angular α of the narrow band signal of i incident _iAnd β _iCorresponding direction vector, the expansion form is expressed as:

a _n(α _i)=(1,exp(j2πd·cosα _i/λ),...,exp[j2πd·(N-1)·cosα _i/λ]) ^T

a _m(β _i)=(1,exp(j2πd·cosβ _i/λ),...,exp[j2πd·(M-1)·cosβ _i/λ]) ^T

4) the noise subspace U of calculating aerial receiver echoed signal Y (t) _n

5) structure angle solved function minV (α _i, β _i), V (α wherein _i, β _i) be:

$V({\mathrm{\&alpha;}}_i,{\mathrm{\&beta;}}_i)=a_m^H\left({\mathrm{\&beta;}}_i\right)G\left({\mathrm{\&alpha;}}_i\right)a_m\left({\mathrm{\&beta;}}_i\right)$

Wherein, $G\left({\mathrm{\&alpha;}}_i\right)=[a_n\left({\mathrm{\&alpha;}}_i\right)\&CircleTimes;I_M{]}^H{U}_n{U}_n^H[a_n\left({\mathrm{\&alpha;}}_i\right)\&CircleTimes;I_M]$ Be intermediate variable;

6) establish α _iFor (0 °, 180 °] an interior fixed value of scope, according to angle solved function minV (α _i, β _i), obtain as follows β _iValue:

6a) definition intermediate variable b _i=exp (j2 π dcos β _i/ λ), and with its substitution formula V (α _i, β _i) in, obtain formula V (α _i, b _i), to b _iDifferentiate

Obtain 2M-2 root;

6b) exist 2M-2 root in seek amplitude near 1 root as b _iValue, again with this b _iThe following formula of substitution calculates corresponding β _iValue:

${\mathrm{\&beta;}}_i=\arccos \left(\frac{\mathrm{\&lambda;}}{2\mathrm{\&pi;d}}\arg \left(b_i\right)\right);$

7) α _iGet (0 °, 180 °] other interior fixed value of scope, repeated execution of steps 6), obtain corresponding β _iValue;

Many groups α that 8) will obtain _iAnd β _iSubstitution function 1/V (α _i, β _i) obtain corresponding a plurality of V values, in the plane, be origin with (0,0), with many groups of (α _i, V) being x, the y coordinate is drawn the range value point, and each point is linked to each other, and obtains the amplitude spectrogram;

9) seek front I larger spectrum peak of amplitude according to order from high to low from the amplitude spectrogram, the x coordinate that the peak point at these spectrum peaks is corresponding is as the α that tries to achieve _iValue is used these α _iCorresponding β _iAs the β that tries to achieve _iValue is finished based on the 2-d direction finding angle of antenna uniform planar battle array and is estimated.

2. the 2-d direction finding angle method of estimation based on the uniform planar battle array according to claim 1, wherein, the noise subspace U of the described calculating aerial receiver of step 4) echoed signal Y (t) _n, carry out as follows:

4a) covariance matrix R=E[Y (t) Y (t) of calculating aerial receiver signal ^H], E[wherein] expression asks mathematical expectation;

4b) covariance matrix R is carried out feature decomposition:

$R=U_s{\mathrm{\&Lambda;}}_s{U}_s^H+U_n{\mathrm{\&Lambda;}}_n{U}_n^H,$

Wherein, Λ _sBe I the eigenvalue matrix that large eigenwert forms of covariance matrix R, Λ _nBe the eigenvalue matrix that covariance matrix R (NM-I) individual little eigenwert forms, U _sFor I the large corresponding feature matrix of eigenwert, be defined as signal subspace, U _nFor the corresponding feature matrix of (NM-I) individual little eigenwert, be defined as noise subspace.

3. the angle method of estimation based on antenna uniform planar battle array according to claim 1, wherein step 6a) described formula V (α _i, b _i) to b _iDifferentiate

Obtain 2M-2 root, carry out as follows:

6a1) with formula V (α _i, b _i) expand into:

Wherein, g ₁₁, g ₁₂... g _MMBe intermediate variable G (α _i) each element in the matrix;

6a2) according to formula V (α _i, b _i) expansion, with formula V (α _i, b _i) to b _iDifferentiate

Expand into:

$\frac{\&PartialD;}{\&PartialD;b_i}V(a_i,b_i)=(M-1)g_{1M}{b}_i^{M-2}+\&CenterDot;\&CenterDot;\&CenterDot;+(g_{12}+g_{23}+\&CenterDot;\&CenterDot;\&CenterDot;g_{(M-1)M})+0+$

$(-1)(g_{21}+g_{32}+\&CenterDot;\&CenterDot;\&CenterDot;g_{M(M-1)})b_i^{-2}+\&CenterDot;\&CenterDot;\&CenterDot;+(-M+1)g_{M1}{b}_i^{-M}=0$

6a3) to above-mentioned steps 6a2) equation find the solution, obtain 2M-2 root.

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